A physics class I once taught stood out from all the others.  The students had an outstandingly low talent for science.  When I put the "bouncing ball" question on their first exam, to see how well they understood acceleration, they surprised me by getting 50% correct—pure guess!  All my other classes got 5% correct because they had learned "the answer" for the top of the bounce.

As the semester wore on, I worked with many of those students to try to find out where their difficulties lay.  The difficulties were deep.  Ratio and proportion was unintelligible for many.  For most, sorting relevance from irrelevance had no meaning, with one-to-one cause and effect being their limit of understood complexity.  A few had difficulty with even that.  Newton's law of action and reaction was seen as a one-to-one cause-effect statement, and the mutual reciprocity central to that law—and which leads to the inseverablity of components which actually is the law—was a non-thought, a gap, in their thinking.  The gaps were many.

Anyone who truly understands the elementary concepts of physics will, when talking with these students, quickly sense that these are people who apparently cannot discuss even the simplest of physics intelligibly.  Their conversations reveal a peculiar "blindness" to the foundations of the subject.  That "blindness" is "obvious."  (I believe that this class came from a more anti-intellectual culture that any other class I had taught, and that they could have achieved greater understanding had their culture embraced intellectual effort.)

One student in this class stood out as special.  The rest of the class deeply resented their "special" student.  She was a small, eager student who obviously was stunted in her growth.  She was eighteen years old but looked twelve or thirteen.  And she asked a lot of questions during lectures and would not quit asking questions until she was sure she understood my answers.  She was not of the anti-intellectual culture of her classmates.

The rest of the class resented her because her questions revealed that she was also stunted in her mental development.  Her limitations were obvious to everyone in the class—except to herself.

On one exam, Ms. Turner (I'll call her that for reasons which will become obvious) stated her carefully reasoned version of Newton's first law of motion.  Newton's version conveys this meaning: An object retains whatever velocity it has until a force acts upon it to change that velocity.

Ms Turner's version was this: An object has a constant velocity until its velocity changes.

She came to me afterward to argue that her statement is better than Newton's.  She had worked long and hard on Newton's statement but couldn't make any sense out of it.  So she reinterpreted it in terms that she could understand.

On another exam she rewrote "Energy can be neither created nor destroyed" to read "Anything created cannot be destroyed." 

This student worked much harder than any of the other students in this class. She was determined to become a nurse's assistant and so I worked hard with her to help her, and eventually my wife came with me to class to give her further help.  She had some learning ability, perhaps about as much as the others in her class.  She had no ability for abstraction, as might be defined by Piaget's "formal operations" concept.  I had given the class a test for formal operational insight that was designed by a psychologist at the university.  The class average was about half the maximum score (about 17 max, I recall).  Ms Turner scored zero, possibly the first person ever to achieve that score.

Ms Turner's failure to see concepts was obvious to her classmates, but her classmates consistently failed to see concepts that are only a slight step deeper in abstraction.  I could see those failures in all conversations with them.  They had no sense of what they were missing.  Just like Ms. Turner. 

"Ms. Turner" had Turners syndrome, a genetic condition in which the normal XX chromosome is lacking the second X.  This inhibits adolescence by blocking production of estrogen.  Estrogen is necessary for both sexual maturation and for certain intellectual developments in the brain that occur at adolescence.  (The developing male brain produces estrogen from testosterone during adolescence.)  These are the most "advanced" of human intellectual developments and the source of science. 
 

Richard Feynman's weekly Hughes Aircraft Company seminars had a lot in common with my various physics classes.  But the subject matter was two or three steps of abstraction deeper, and that placed those seminars at the other end of some scale of human "seeing."

Feynman saw things almost no other human being could see.  We saw him as a "magician" who often did things totally outside our ability to conceptualize.  His way of solving differential equations was utterly opaque and mysterious to me, and, I think, to most of our group.  One thing that I, many decades later, did come to see illuminates a little about "seeing."  It was the "dimensionality" of color vision.

When we presented Feynman with the new Scientific American showing Edwin Land's two-photo reproduction of apparently three-factor color, Feynman declared, "I don't think the three-factor color theory is any danger."  We thought he was wrong.  It took a lengthy (for then) computer analysis to show he was right.  A year later.

Feynman's insights about color lay in the depths of mathematical analysis, in the subtleties of Hilbert Space.  A few years later, Feynman put into his The Feynman Lectures on Physics an ingenious, easily understood, graphical picture of the Hilbert space relationships between "normal," (three-cone) color vision and the two, common, two-cone colorblindnesses, protanopia and deuteranopia.

I became immersed in Hilbert Space a few years after that Wednesday afternoon seminar, but it still took me much more effort with the puzzles of dimensionality and color vision before I saw at least something of what Feynman had seen after a minute or so of thinking about the question.

(We've posted a series of Web pages to guide a Web surfer toward some of the insights—see below.  Those pages seem not to be very successful as guides to an unknown territory.  However, they do make a good test for a person's skill at seeing this one underpinning of modern science and a good exercise that could extend that perception—of the abstract—a little deeper.)

Ms. Turner and Feynman were far apart in what they can see, but both were human, their thinking human.  They were both products of human evolution, a process that advances by steps into more effective thinking—while pruning the ineffective thinking.

Think about it.

Dimensionality is a very simple concept, but it is beyond the edges of easy human comprehension.  It's also a concept that reaches deep into human life and the way we "see" the world we have to interact with.  Many of the Nobel Prizes in Economics, the newest of the Nobel's, have been for insights into dimensionality.  That puts it squarely in the realm of politics and economics as well as in the realm of physics and psychology.

That it produced Nobel Prizes demonstrates that it requires human thinking and insight operating at its farthest outreach. 

However, anyone who does "see" the implications of dimensionality can, when discussing it with another, see whenever the other does not "see."  Just like my "special" class could see that Ms. Turner was missing things.  Just like I could see that my special class did not see acceleration and Newton's laws of motion.  Just like Feynman could see that we, his class, could not see how he solved differential equations.

And just like a color "normal" person can see that a protanopic colorblind person is missing seeing, for example, a difference between orange and grass green.  (That's one reason for color vision being such a good exemplar for comparing human "seeing" with "logic blindness.")

Human information processing is a genetically guided set of developments that starts with many endocrine processes, such as enzyme and hormone interactions, extends to neurological processes that include our perceptions and our "mental" processing, and culminates in selecting from alternatives of interactions with the world in ways that let us anticipate the outcomes.  Those outcomes which give us advantages are those that keep us in the evolutionary race.
 

Prejudice and bigotry guide human cultures to human misery.  No one sees himself or herself as being a bigot or holding prejudiced views. Other people are bigots.  I am committed to freedom, justice, and [choose as many as you wish] democracy, liberty, peace, principles, courage, truth, God, morality, ...

Several decades ago a social psychologist paired off students who had taken a personality inventory and scored at the extremes on a scale of prejudice.  The experiment was simple: each pair of  students, one scoring high in prejudice, one low,  talked to each other for ten minutes about anything that came into their minds.  Then they were handed another personality test and asked to answer it, not as they would answer it, but as the person they had talked with would answer it.

All the test papers were answered similarly, indicating high prejudice.

At least in this experiment, prejudice partners with inability to see as other people see.

Freedom without equality is an egocentric, perhaps ethnocentric, desire born of blindness to the needs of the "others." It is destructive to all humanity and seen as evil by too few.

"I know of many boys who will refuse to go into the army.  They don't want to go to war and do the same things to other innocent people that happened to us."

"I feel that I must join the army and help my country."
"My parents were hippies: I was raised as anti war and with liberal beliefs."
"I don't want to die, but that's one of those things that might happen.  It just has to be."

I believe many people will see that the recruit had simply missed the meaning in what the girl had said.  They will sense the recruit's "blindness" to the mutual reciprocity seen by the girl.  Herein lies the insight of Lawrence Kohlberg that brought him a barrage of bitter rancor. 

And many will not see these things.

"Freedom," as used today usually lacks information content.  It's abstractness lets anyone who is blind to the abstractness use it to mean anything:

Anyone hates the freedom of their enemy to kill them with impunity.
Ethnocentric groups easily see any killing they do as self-defense, perhaps even as "the only moral imperative possible" (journalist comment on radio as I write this).

Unless this positive feedback loop is broken, human cultures will become victim's of their ethnocentrism. 

Human evolution encounters a crossing of paths here.  Superior killling skills and superior information processing, "intelligence," conflict.  Some people choose killing, a seemingly correct choice when self is seen as superior in all the scales seen as significant. 

But some people see more scales than others see.  Some people see when "humanity" must be substituted for "my country."

Politician #1 spoke of "freedom and equality."  Others often speak only of  freedom. 

"Equality" is a concept that straddles the edge of human comprehension.

To many, "equality" means only "the same":  Two values that we have measured are "equal" when they are identical.  Five equals five.  Seventeen equals seventeen.  That cannot be the meaning of "equality" when comparing people, and many people sense this deep truth.

But too many people sense nothing of these deep truths, truths which recognize that to say one person "is better than" another depends on so many, many different recognitions of "it depends..."  That is to say, they do not "see" the roots of the scientific concept of "dimensionality."  And when they see  that "people are different," they tragically conclude that "equality" is, therefore, nonsense.  They sense that they must reject equality in the sense that Politician #1 was speaking of.

Meaningful measure of "value" of people must be richly multicomponented.  People can not be lined up by their worth without first reducing the complexity of "worth" to a single dimension, to a useless scrap of meaning.  Value of people has meaning only in spaces of many, many dimensions.  And that's only the beginning: we need the further complexity expressed by tensors in their appropriate Hilbert Space.

We need not have knowledge of Hilbert Space to sense this deep, multidimensional truth, and many people, like Politician #1, do sense it.  They are compelled by that sense to link freedom always to equality because if we don't, we open wide the doors to egocentric and ethnocentric bigotry.  "Fairness" quickly degrades to no better than "Is it good for me?"  "Justice," loses its essential meaning of "without bias," leaving it dangling freely to pick up its popular meaning of "revenge."

"See like a bird" conveys a wonderful meaning, a meaning which, if widely understood,  could save humanity from mutually reciprocal destruction born out of the pinched view of ethnocentrism.